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I was thinking like you. Once I saw the picture. You clearly have something that looks like an integral with limits.

mate you don't need to use up half the screen to show your face typing. you're not photogenic and no one comes here thinking you are, just focus more on the content and reducing the dead air.

In your other video "what did we all miss in this 2000 year old problem" where you explained how the Johnson-Jackson girls proved the Pythagorean theorem using trigonometry. In it you said "let us assume A and B are not equal." Well, that is a hypothesis, so you haven't proven a thing. Then, they began their proof using two right triangles which is basic geometry and you even mentioned algebra. They may have somewhat proved the theorem using trigonometry, but they began by using geometry. One cannot get to the moon w/o going up. You cannot get to 3 w/o going through 2. Without algebra and geometry, there is no trigonometry.

You make geometry, my favorite subject, seem unnecessary. So, the girls used only trigonometry to create this so-called new proof? What did they initially start with?, a right triangle, which is geometry. I applaud their effort, but you cannot get to the moon w/o going up. One cannot get to 3 w/o going through 2. 1+1.9 does not equal 3, only 1+2=3.

In the 60 Mintes video, it was stated that they only used trigonometry to creat this proof. So, they used only trigonometry to create this so-called new proof? What did they initially start with?, a right triangle, which is geometry. I applaud their effort, but you cannot get to the moon w/o going up. One cannot get to 3 w/o going through 2. 1+1.9 does not equal 3, only 1+2=3.

You’re just going to ignore the Runge phenomenon

I have tried KAN in 2 prediction problems: SOC estimation and chiller energy consumption prediction. It works.

Runge-Kutta just wasn't clicking for me. This video helped a lot. Thanks!

You are nuts! Apostol's Analysis has the hardest exercises ever because it expects you to know things that are not covered in the book or in any calculus book that you've been through! Ever encountered the Vieta's formulas for sums of roots in an ordinary calculus textbook? I don't think so...

A lot of Thales beliefs come from Kemet. The understanding would go on to become hermetic teaching. This possibly came from the Kemetic schools being expressed as exonyms.

Isn't the definition at the beginning of the function where when x=y we get 1, and when x!=y we get 0, is this not a definition of the Kronecker Delta? Just curious.

Hii thank you so much for the video. Can you please do the implementation of KANs?

Unfortunately I solved it... Check bottom of post for certain explanations This Is To Eliminate Numbers that dont need to be Checked: Given Arithmetic progression, x to be all numbers, x => 1,2,3,4,5,... Eliminating all odd numbers, leaves 2x => 2,3,4,5,... Removing all numbers divisible by 4 [a] rewrites the equation to 4x-2 => 2,6,10,... [b] Inserting into the congecture, leaves 2x-1 => 1,3,5, 7,... [c] Infinite Elinimination: for any funtion f(x)=nx-1 [e.g. 2x-1] f(x)==>3[f(x)]+1==>3[f(2x)]+1==>(3[f(2x)]+1)/2)==>f(x) eg continuing with 2x-1 and compared with nx-1 2x-1 OR nx-1 > 3(nx-1)-1 3nx-2 > 3n(2x)-2 6nx-2 > (6nx-2)/2 3nx-1 [d] EXPLANATION: a- checking for numbers divisible by 4 will always end you up on a previously checked number. b- the expressions are REWRITTEN to fit the Arthmetic sequence c- the entire progression are even numbers d- since n represents any number at all it means the cycle can repeat repeatedly until the set of all integers are eliminated

Thank you for this incredibly informative video on Kolmogorov Arnold Networks! 🤯💻 It's such a deep dive into machine learning concepts, and I appreciate how you break down complex ideas into understandable explanations. 🌟 I'm curious about the future direction of your channel. 🚀 Are there plans to delve deeper into specific machine learning architectures like Kolmogorov Arnold Networks, or will you explore a broader range of topics within the field? 🤔📈 Additionally, do you have any upcoming collaborations or special projects in the pipeline that your viewers can look forward to? 🌐🔍 Keep up the fantastic work!

Not about the proof, but Pythagoras lived approximately 2500 years ago.

Would this apply only to the Florida state schools? Or to private institutions as well? That is where the great research will concentrate if tenure is taken away from public institutions.

do you have any machine learning theory courses that follows this series of videos? I would happy to see a Machine learning theory course from you.

Hello. What if the gram matrix is Positive semi-definite. i.e., at least one eigenvalue is zero. Then how do we find the weights? - I believe the matrix is not invertible. Do we use factorization techniques LU factorization to approximate the weights?

I've tried my hand at the Collatz Conjecture recently as well for a bit and I was excited to see someone also come up with the idea of representing the original integer as a sum of powers of two divided by 3^m. Other things I did was noticing that 2^n-1 always goes to 3^n-1, and noticing that repeated division by two is similar to modular arithmetic, as you're looking at the multiplicative remainder of log2(x). After that I was looking for a way to decompose log2(x+y) and got on tangent about the operation x⌄y=ln((e^x+e^y)/2), which distributes addition, i.e. c+(x⌄y)=(x+c)⌄(y+c), and looked at what happens when you change the base, which I found is best to do with ((nx)⌄(ny))/n, as when n -> infinity the operation become max(x,y), when n -> -inf it becomes min(x,y) and when n -> 0 it becomes (x+y)/2. Looks like a paper bending up and down on the 3D graph and it is basically just a bunch of ln(cosh(nx))/n stacked next to each other translated linearly

KAN draws inspiration from the Kolmogorov-Arnold representation theorem, though it significantly diverges from and falls below the theorem's original intent and content. It confines its form to compositions of sums of single-variable smooth functions, representing only a tiny subset of all possible smooth functions. This confinement eliminates, by design, the so-called curse of dimensionality. However, there is no free lunch. It is seriously doubtful that this subset is dense within the entire set of smooth functions --- though I have not come up with an example yet. If it is indeed not dense, KAN will not serve as a universal function approximator, unlike the multilayer perceptron. Nonetheless, it may prove valuable in fields such as scientific research, where many explicitly defined functions tend to be simple, even if they do not approximate all possible smooth functions.

I learned so much today. Btw, can I say that I *love* that Spider-Man poster behind you 😁

Hold on, I'm reading Wikipedia, turns out that Karatsuba (the one who invented his multiplication algorithm) is a student of Kolmogorov!!!

Super interesting. This is something I have been thinking about a lot recently. I wonder how it would be possible to combine this method with further observables that have a strong influence on the actual trajectory. It seems this method is able to derive the "true"/most likely trajectory from many examples of trajectory start-/endpoints alone, but of course it would be much more powerful if it were able to make use of other correlated observations as well. What are your thoughts on this?

Both Russian scientists? Kolmogorov is OK, but "Arnold" does not sound like a Russian surname at all.

This is unbelievable!! Thanks for this very beneficial deep dive. I can not thank you enough for the second website for data acquisition! I was genuinely struggling since the first website seems to be temporarily closed! Keep up the fantastic work!

Right…..

I don't think there's anything in principle preventing a KAN layer or layers from being put inside a normal deep network. So there may be a space of interesting hybrids that do interesting things. For example, the time-wise sum of a time- wise convolution with a (2 layer?) can learn to perform attention, without needing all those horrible fourier features.

thanks

what is r1?

Appreciate your effort making serious videos

The way you teach is impressive. I have been around understanding all this and finally came into your channel.

Hlo! (54 yr old) taking graduate level numerical analysis in the fall. Any suggestions how to prepare over the summer?

4:19 i have exact same book in my library but never made a connection tbh that current KAN hype in AI world is connected the same Arnold

I am a retired teacher of secondary school maths in the UK. I couldn't have done this. Well done, ladies😍

fresh eyes! congrats!! goes further back to Egypt

Man, what a channel. Awesome to find videos not shying away from technical topics.

Thanks for the video, I'd attacked the problem awhile after you and had followed a similar path. Nice to see that I wasn't totally off base even if I got stuck a bit before you put together your inverted representation!

I enjoy your videos. I have a bachelor's in mechanical engineering and have been out of school working for 10 years. I always loved math and wanted to take real analysis in school but it dudt work out. For the past few month I have been going thru calc again with George Simmons book with the hopes of going thru understanding analysis by Abbott after that.its so satisfying when your work hard on a problem and finally get it. Looking forward to more videos

I take an applied math perspective and a nonrigorous one at that. I don't use the Nyquist theorem as a theorem pe se, but as a criterion or requirement for sampling a band-limited signal fast enough so that periodic images of the sampled signal do not overlap in the frequency domain. I prove Shannon's sampling theorem as a special case of the convolution theorem when one of the functions is an ideal sampling function (Dirac comb). Sampling a band-limited signal (compact support in the frequency domain) results a function with a periodic spectrum by application of the convolution theorem and the fact the Fourier transform of a Dirac comb is also a Dirac comb (but in the frequency domain). Convolving a Dirac comb with a bandlimited signal results in a function with a periodic spectrum. QED. The Nyquist criterion then becomes the requirement the signal be sampled fast enough to spread the periodic images of the sampled signal apart in the frequency (so the images do not overlap in the frequency domain and cause frequency folding).

i think that KAN will be stronger than MLP in physics informed neural networks

the square within a square is a more elegant proof.

I thought the point was to embed a core logic to reduce size.

Do you think no one else made an attempt before them as opposed to couldn't figure it out. There was a guy in 2009 that also found the answer.

Hey, great video. If you take constructive(?) criticism (and you may have already noticed when editing), you should reduce the sensitivity of focus adjustment of your recording device, or set it to a fixed value. It tries to focus the background (computer screen) and foreground (your hands) instead of you.

Great video! Eagerly awaiting your next one! :)

its an old method from 2021: ruclips.net/video/eS_k6L638k0/видео.html

This sort of high level discussion is always seductive. I look forward to the nuts and bolts to see whether the first date performance can be sustained.....

I'm here after the 60 Minutes story finally arrived in my content algorithm... an entire year after-the-fact. Apparently I've been focused on old-white-male-politics for the past few years to be rewarded with content I actually like.

Who needs maths when AI does it all for us. Oh... yeah... it's not AI. :) It's MATHS! :)

awesome vid man